= Aromatic-hydrogen counting in tocopherol identification
\b[Aromatic-hydrogen counting in tocopherol identification] uses unoccupied ring positions to constrain the identity or composition of a <tocopherol> sample. In the <tocol> framework, positions 5, 7 and 8 can carry the additional methyl substituents. The familiar <alpha-tocopherol>, <beta-tocopherol>, <gamma-tocopherol> and <delta-tocopherol> substitution patterns leave respectively zero, one, one and two hydrogens at those positions.<Nomenclature of Tocopherols and Related Compounds by IUPAC-IUB Joint Commission on Biochemical Nomenclature>[Recommendations 1.2 and 2–5]{ref}
Let $k$ count those aromatic methyl substituents. The count $n_{\mathrm{arH}}=3-k$ concerns aromatic carbon-bound hydrogens. It excludes the hydroxyl hydrogen and hydrogens on the saturated ring and side chain. A missing aromatic hydrogen is not a missing hydrogen atom from the entire molecular formula: replacing ring H by $\mathrm{CH_3}$ adds two hydrogens overall.
A <proton nuclear magnetic resonance> experiment can compare an integrated aromatic region with a calibrated amount standard. For a sufficiently resolved, quantitatively acquired signal, integrated response tracks the number of contributing protons; the count does not predict the number of separately resolved peaks. <Chemical shifts>, splitting, spectral overlap and acquisition conditions remain part of identification.
An original <mixture> example illustrates <mixture ambiguity in aromatic-proton counts>. Suppose the calibrated aromatic response corresponds to $r=1.30$ hydrogens per <tocopherol> molecule. If the sample contains only <beta-tocopherol> and <delta-tocopherol>, and $x$ is the <mole fraction> of <delta-tocopherol>, then $r=(1-x)+2x=1+x$, giving $x=0.30$. The same count occurs in a <gamma-tocopherol>/<delta-tocopherol> mixture. If the allowed components are instead <alpha-tocopherol> and <delta-tocopherol>, $r=2x$ gives $x=0.65$. Counting alone does not identify an unrestricted mixture.
In particular, <beta-tocopherol> and <gamma-tocopherol> are <constitutional isomers> with one remaining aromatic hydrogen each, at different ring positions. Their count agrees while their structural assignment differs. A useful experiment therefore combines the aromatic integral with resolved <chemical shifts> or other structural evidence and specifies which candidate components were allowed. These are predictions from the named structures, not measured spectra or universal instrumental settings.
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